It was likely a hard decision for Odorizzi, who was hoping to land a multi-year deal following an All-Star, career-best season in which he went 15-7 with a 3.51 ERA and 178 strikeouts in 159 innings while holding opponents to a.231 batting average.
Just 10 free agents received the offers on November 4, and their former teams will receive draft-pick compensation if they sign elsewhere before the amateur draft in June.
There aren't any surprises in that list, as there wasn't doubt that Bumgarner, Cole, Donaldson, Rendon, Strasburg, and Wheeler would forego the one-year offer in search of a much richer, multi-year commitment. He can become a free agent again after the 2020 season, when there will be no loss of draft picks attached and fewer high-level starting pitchers competing for attention.
The first domino in MLB's offseason pitching market has fallen.
Two free-agents-to-be have accepted qualifying offers from Major League Baseball clubs, which is two more than some years.
Odorizzi, 29, was 15-7 for the Twins last season with a 3.51 earned run average and 178 strikeouts in 159 innings pitched.
Abreu, who made his third All-Star team in six seasons with the White Sox, led the AL with 123 RBIs last season while batting.284 with 33 home runs. An eighth free agent, Will Smith, rejected the Giants' qualifying offer and left the free agent market even before the deadline passed, signing a three-year, $40MM deal with the Braves.
Relief pitcher Will Smith, who also declined the offer, signed with the Atlanta Braves on Thursday.
The 30-year-old Smith went 6-0 with a 2.76 ERA and a career-best 34 saves for the San Francisco Giants this past season. The Braves re-signed outfielder Nick Markakis, catcher Tyler Flowers and reliever Darren O'Day.